Accelerated Circulant and Skew Circulant Splitting Methods for Hermitian Positive Definite Toeplitz Systems
نویسندگان
چکیده
منابع مشابه
Accelerated Circulant and Skew Circulant Splitting Methods for Hermitian Positive Definite Toeplitz Systems
We study the CSCS method for large Hermitian positive definite Toeplitz linear systems, which first appears in Ng’s paper published in Ng, 2003 , and CSCS stands for circulant and skew circulant splitting of the coefficient matrix A. In this paper, we present a new iteration method for the numerical solution of Hermitian positive definite Toeplitz systems of linear equations. The method is a tw...
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for solving large sparse non-hermitian positive definite linear equations, bai et al. proposed the hermitian and skew-hermitian splitting methods (hss). they recently generalized this technique to the normal and skew-hermitian splitting methods (nss). in this paper, we present an accelerated normal and skew-hermitian splitting methods (anss) which involve two parameters for the nss iteration. w...
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We study the solutions of Hermitian positive deenite Toeplitz systems Ax = b by the preconditioned conjugate gradient method for three families of circulant preconditioners C. The convergence rates of these iterative methods depend on the spectrum of C ?1 A. For a Toeplitz matrix A with entries which are Fourier coeecients of a positive function f in the Wiener class, we establish the invertibl...
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Comparing the lopsided Hermitian/skew-Hermitian splitting (LHSS) method and Hermitian/skewHermitian splitting (HSS) method, a new criterion for choosing the above two methods is presented, which is better than that of Li, Huang and Liu [Modified Hermitian and skew-Hermitian splitting methods for nonHermitian positive-definite linear systems, Numer. Lin. Alg. Appl., 14 (2007): 217-235]. Key-Word...
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We study the solutions of Hermitian positive definite Toeplitz systems Tnx = b by the preconditioned conjugate gradient method. For preconditioner An the convergence rate is known to be governed by the distribution of the eigenvalues of the preconditioned matrix A−1 n Tn . New properties of the circulant preconditioners introduced by Strang, R. Chan, T. Chan, Szegö/Grenander and Tyrtyshnikov ar...
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ژورنال
عنوان ژورنال: Advances in Numerical Analysis
سال: 2012
ISSN: 1687-9562,1687-9570
DOI: 10.1155/2012/973407